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I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it?

I can understand the Pareto set and contract curve but when it comes to equilibrium I'm stuck.

For ex. if we have two consumers: Consumer 1 has as his initial bundle all of good $2:(0; 10)$ ; while consumer 2 has all of good $1 : (10; 0)$.

Let their utilities be $$u_1= min (x; y)$$ $$u_2= min (4x; 5y)$$

What would be the steps for finding the offer curves? Appreciate any help given.

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In the picture below offer curve of individual 1 is given by lines connecting $E$ to $O_1$ and $O_1$ to $O_2$. And offer curve of individual 2 is given by lines connecting $E$ to $O_2$ and $O_2$ to $A$ and $A$ to $O_1$. Set of competitive equilibria are given by the intersection of two offer curves. $p_X = 0$ and $p_Y = 1$ supports allocation at $O_2$ as competitive equilibrium. Allocations on the line segment $O_1A$ are supported by prices $p_X = 1$ and $p_Y = 0$.

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  • $\begingroup$ Thank you for your solution. Could you please suggest to me some literature regarding the offer curves so as to find the general equilibrium? $\endgroup$
    – Maybeline Lee
    Commented Jan 22, 2021 at 13:27
  • $\begingroup$ Chapter 15 General Equilibrium of Microeconomic Theory by Mascollel, Whinston and Green $\endgroup$
    – Amit
    Commented Jan 22, 2021 at 15:14

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